Photonic Band Structures Calculation Of Two-Dimensional Photonic Crystals

In this thesis, photonic band structures of many different types of two-dimensional (2D) photonic crystals have been calculated based on plane-wave expansion (PWE) method. Firstly, by using frequency independent PWE method, 2D dielectric photonic band structures in simple lattices, complex lattices and defect lattices were calculated respectively. Two types of 2D complex lattice photonic crystals, which owned 2D complete photonic band gaps were investigated. Then, combined with supercell technique, defect modes of 2D photonic crystal wave guides were calculated. We found that because of the existence of defect modes, the photonic band gap in E-polarization band structures disappeared. And, the influence factors on photonic band structures, such as the width of the defect and the number of rods on both sides of the defect, were discussed.Secondly, by using frequency dependent PWE method, we realized numerical calculation toward 2D metal and plasmonic photomc crystals, in which the dielectric constants depended on electromagnetic wave frequencies. Comparing our results and those in published papers, we verified our calculation programs. Based on these progresses, we developed present frequency dependent PWE method and calculated 2D high-temperature superconductor (HTSC) photonic crystals. Contrary to results in published papers, we found that the tunability of photonic band structures by changing temperature was actually very little. In our calculation, we considered the contribution of normal conducting electrons which formal papers omitted it, so our calculation were closer to real situations and obtained more accurate results. We found that the contribution of normal conducting electrons can not be omitted with increasing temperature, especially approaching the critical temperature of HTSCs.Finally, based on frequency dependent PWE method and Maxwell-Garnett type effective medium theory, 2D metal-dielectric (MD) photonic band structures were investigated. In the case of E-polarization, when the thickness of metal coating was greater than a critical value, band structures of MD photonic crystals were almost the same as those of metal photonic band structures, expect several flat bands. In the case of H-polarization, if the metal coating was thick enough, the lowest frequency band gap between the first and the second bands would appear. According to Maxwell-Garnett type effective medium theory, we predicted that the existence of the lowest frequency band gap was independent with lattice geometry, and it was not due to Bragger scattering as traditional dielectric photonic crystals did, but because of the individual metal coated rods. Then, we calculated 2D MD photonic band structures in different lattice. These calculation results accorded with our prediction.